Nonlocal regularization models have been shown to outperform pixel-based regularization for inverse problems such as superresolution, inpainting, and compressed sensing [1]}, [2]}, [3]}, [4]}.
The challenge with nonlocal regularizers is to come up with efficient iterative algorithms.
Split Bregman is used in [2]}, alternating minimization in [3]}, [1]}, and half-quadratic splitting in [4]}. However, except for [2]}, the regularizer in [1]}, [3]}, [4]} are nonconvex and the algorithms do not come with any convergence guarantee. The regularizer in [2]} uses pixels to measure nonlocal variations.
As explained in Section , computational challenges arise in extending the split Bregman optimizer (which is similar to ADMM) in [2]} to handle patch-based variations.
